Question: Simplify; express your answer in exponential form. Assume $r\neq 0, x\neq 0$. $\dfrac{{(rx^{5})^{-4}}}{{(r^{3}x^{-4})^{-3}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(rx^{5})^{-4} = (r)^{-4}(x^{5})^{-4}}$ On the left, we have ${r}$ to the exponent ${-4}$ . Now ${1 \times -4 = -4}$ , so ${(r)^{-4} = r^{-4}}$ Apply the ideas above to simplify the equation. $\dfrac{{(rx^{5})^{-4}}}{{(r^{3}x^{-4})^{-3}}} = \dfrac{{r^{-4}x^{-20}}}{{r^{-9}x^{12}}}$ Break up the equation by variable and simplify. $\dfrac{{r^{-4}x^{-20}}}{{r^{-9}x^{12}}} = \dfrac{{r^{-4}}}{{r^{-9}}} \cdot \dfrac{{x^{-20}}}{{x^{12}}} = r^{{-4} - {(-9)}} \cdot x^{{-20} - {12}} = r^{5}x^{-32}$